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Goldie criteria for some semiprime rings

Published online by Cambridge University Press:  18 May 2009

K. A. Brown  and
B. A. F. Wehrfritz
K. A. Brown
Affiliation:
Department of Mathematics, University of Glasgow, Glasgow G12 8QW
B. A. F. Wehrfritz
Affiliation:
School of Mathematical Sciences, Queen Mary and Westfield College, London E1 4NS
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We principally consider rings R of the form R = S[G], generated as a ring by the subring S of R and the subgroup G of the group of units of R normalizing S. (All our rings have identities except the nilrings.) We wish to deduce that certain semiprime images of R are Goldie rings from ring theoretic information about S and group theoretic information about G. Usually the latter is given in the form that G/N has some solubility or finiteness property, where N is some specified normal subgroup of G contained in S. Note we do not assume that N = G∩S; in particular N = 〈1〉 is always an option.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 33 , Issue 3 , September 1991 , pp. 297 - 308
Copyright
Copyright © Glasgow Mathematical Journal Trust 1991

References

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